The simplest possible model is proposed to explain a large fraction of the millennial climate variability measured in the isotopic composition of Antarctic ice cores. The model results from the classic bipolar seesaw by coupling it to a heat reservoir. In this ``thermal bipolar seesaw'' the heat reservoir convolves northern time signals with a characteristic timescale. Applying the model to the data of GRIP and Byrd, we demonstrate that maximum correlation can be obtained using a timescale of about 1000-1500 years. Higher correlations are obtained by first filtering out the long-term variability which is due to astronomical and greenhouse gas forcing and not part of the thermal bipolar seesaw. The model resolves the apparent confusion whether northern and southern climate records are in or out of phase, synchronous, or time lagged.